Like Amu Hinamori's attack as Amulet Spade, Colorful Canvas, he uses the paintbrush's paint by spinning it in his paw and throwing out rainbow colored paint. This also serves to trap anything in the paint.
However, Kwazii can also use the Mystic Paintbrush to paint anything he wants and then turn it real. And in Paint Me A Prediction, he can use the paintbrush to paint predictions that see to come true.
The phrase goes by "Here's paint in yer' eyes!".